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### Generalizations of Boolean posets/lattices

A Boolean lattice has a number of rather nice properties which give it a central role in many parts of combinatorics. For instance, it's a lattice, it can be augmented with a ring structure, it can ...

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### What's a non-abelian totally ordered group?

Because I have heard the phrase "totally ordered abelian group", I imagine there should be non-abelian ones. By this I mean a group with a total ordering (not to be confused with a well-ordering) ...

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### Automorphisms of the totally ordered group Z^n with lexicographical order

It is easy to see that the totally ordered group Z (the integers) with the natural order has no non-trivial automorphisms. Is this also true for Z^n with the lexicographical order?

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### Chains intersecting antichains in finite posets

I feel a little embarrassed to be asking this question here, since I think it should be much easier than I'm making it, but here goes:
Given a finite poset P, does there necessarily exist some chain ...

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### Is there a “universal LYM inequality?”

This question is based on a blog post of Qiaochu Yuan.
Let P be a locally finite* graded poset with a minimal element, and w be a weight function on the elements of P. Suppose that the total weight ...

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### Questions about ordering of reals and irrationals

Three problems from G.Rosenstein "Linear orderings" (from the end of Chapter 2 and beginning of Chapter 4):
1) Is there a nondecreasing function from irrationals onto reals?
2) Is there a ...